OCMEBilingual mathematics & derivations繁體中文

Possible Outcomes, Recording Fibers, and Completeness

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batch-20261008-advance-20261011-r06-sample-space-foundations · 2026-10-08 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

1. All Ordered Elementary Outcomes

First-stage outcomes A=[0], second-stage outcomes B=[0]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[0, 0]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[0, 0]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

2. All Ordered Elementary Outcomes

First-stage outcomes A=[-1, 1], second-stage outcomes B=[0, 2]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-1, 0], [-1, 2], [1, 0], [1, 2]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-1, 0], [-1, 2], [1, 0], [1, 2]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

3. All Ordered Elementary Outcomes

First-stage outcomes A=[-2, 2], second-stage outcomes B=[-1, 0, 3]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-2, -1], [-2, 0], [-2, 3], [2, -1], [2, 0], [2, 3]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-2, -1], [-2, 0], [-2, 3], [2, -1], [2, 0], [2, 3]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

4. All Ordered Elementary Outcomes

First-stage outcomes A=[-3, 3], second-stage outcomes B=[0, 4]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-3, 0], [-3, 4], [3, 0], [3, 4]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-3, 0], [-3, 4], [3, 0], [3, 4]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

5. All Ordered Elementary Outcomes

First-stage outcomes A=[-4, 4], second-stage outcomes B=[-1, 0, 5]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-4, -1], [-4, 0], [-4, 5], [4, -1], [4, 0], [4, 5]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-4, -1], [-4, 0], [-4, 5], [4, -1], [4, 0], [4, 5]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

6. All Ordered Elementary Outcomes

First-stage outcomes A=[-5, 5], second-stage outcomes B=[0, 6]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-5, 0], [-5, 6], [5, 0], [5, 6]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-5, 0], [-5, 6], [5, 0], [5, 6]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

7. All Ordered Elementary Outcomes

First-stage outcomes A=[-6, 6], second-stage outcomes B=[-1, 0, 7]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-6, -1], [-6, 0], [-6, 7], [6, -1], [6, 0], [6, 7]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-6, -1], [-6, 0], [-6, 7], [6, -1], [6, 0], [6, 7]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

8. All Ordered Elementary Outcomes

First-stage outcomes A=[-7, 7], second-stage outcomes B=[0, 8]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-7, 0], [-7, 8], [7, 0], [7, 8]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-7, 0], [-7, 8], [7, 0], [7, 8]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

9. All Ordered Elementary Outcomes

First-stage outcomes A=[-8, 8], second-stage outcomes B=[-1, 0, 9]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-8, -1], [-8, 0], [-8, 9], [8, -1], [8, 0], [8, 9]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-8, -1], [-8, 0], [-8, 9], [8, -1], [8, 0], [8, 9]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

10. All Ordered Elementary Outcomes

First-stage outcomes A=[-9, 9], second-stage outcomes B=[0, 10]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-9, 0], [-9, 10], [9, 0], [9, 10]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-9, 0], [-9, 10], [9, 0], [9, 10]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

11. All Ordered Elementary Outcomes

First-stage outcomes A=[-10, 10], second-stage outcomes B=[-1, 0, 11]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-10, -1], [-10, 0], [-10, 11], [10, -1], [10, 0], [10, 11]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-10, -1], [-10, 0], [-10, 11], [10, -1], [10, 0], [10, 11]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

12. All Ordered Elementary Outcomes

First-stage outcomes A=[-11, 11], second-stage outcomes B=[0, 12]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-11, 0], [-11, 12], [11, 0], [11, 12]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-11, 0], [-11, 12], [11, 0], [11, 12]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

13. All Ordered Elementary Outcomes

First-stage outcomes A=[-12, 12], second-stage outcomes B=[-1, 0, 13]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

14. All Ordered Elementary Outcomes

First-stage outcomes A=[-13, 13], second-stage outcomes B=[0, 14]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-13, 0], [-13, 14], [13, 0], [13, 14]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-13, 0], [-13, 14], [13, 0], [13, 14]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

15. All Ordered Elementary Outcomes

First-stage outcomes A=[-14, 14], second-stage outcomes B=[-1, 0, 15]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-14, -1], [-14, 0], [-14, 15], [14, -1], [14, 0], [14, 15]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-14, -1], [-14, 0], [-14, 15], [14, -1], [14, 0], [14, 15]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

16. All Ordered Elementary Outcomes

First-stage outcomes A=[-15, 15], second-stage outcomes B=[0, 16]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-15, 0], [-15, 16], [15, 0], [15, 16]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-15, 0], [-15, 16], [15, 0], [15, 16]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

17. All Ordered Elementary Outcomes

First-stage outcomes A=[-16, 16], second-stage outcomes B=[-1, 0, 17]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-16, -1], [-16, 0], [-16, 17], [16, -1], [16, 0], [16, 17]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-16, -1], [-16, 0], [-16, 17], [16, -1], [16, 0], [16, 17]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

18. All Ordered Elementary Outcomes

First-stage outcomes A=[-17, 17], second-stage outcomes B=[0, 18]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-17, 0], [-17, 18], [17, 0], [17, 18]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-17, 0], [-17, 18], [17, 0], [17, 18]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

19. All Ordered Elementary Outcomes

First-stage outcomes A=[-18, 18], second-stage outcomes B=[-1, 0, 19]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-18, -1], [-18, 0], [-18, 19], [18, -1], [18, 0], [18, 19]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-18, -1], [-18, 0], [-18, 19], [18, -1], [18, 0], [18, 19]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

20. All Ordered Elementary Outcomes

First-stage outcomes A=[-19, 19], second-stage outcomes B=[0, 20]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-19, 0], [-19, 20], [19, 0], [19, 20]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-19, 0], [-19, 20], [19, 0], [19, 20]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

21. All Ordered Elementary Outcomes

First-stage outcomes A=[-20, 20], second-stage outcomes B=[-1, 0, 21]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-20, -1], [-20, 0], [-20, 21], [20, -1], [20, 0], [20, 21]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-20, -1], [-20, 0], [-20, 21], [20, -1], [20, 0], [20, 21]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

22. All Ordered Elementary Outcomes

First-stage outcomes A=[-21, 21], second-stage outcomes B=[0, 22]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-21, 0], [-21, 22], [21, 0], [21, 22]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-21, 0], [-21, 22], [21, 0], [21, 22]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

23. All Ordered Elementary Outcomes

First-stage outcomes A=[-22, 22], second-stage outcomes B=[-1, 0, 23]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-22, -1], [-22, 0], [-22, 23], [22, -1], [22, 0], [22, 23]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-22, -1], [-22, 0], [-22, 23], [22, -1], [22, 0], [22, 23]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

24. All Ordered Elementary Outcomes

First-stage outcomes A=[-23, 23], second-stage outcomes B=[0, 24]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-23, 0], [-23, 24], [23, 0], [23, 24]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-23, 0], [-23, 24], [23, 0], [23, 24]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

25. All Ordered Elementary Outcomes

First-stage outcomes A=[-24, 24], second-stage outcomes B=[-1, 0, 25]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

View answer and explanation

[[-24, -1], [-24, 0], [-24, 25], [24, -1], [24, 0], [24, 25]]

Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-24, -1], [-24, 0], [-24, 25], [24, -1], [24, 0], [24, 25]].

Reviewed step-by-step derivation

Sample space · qf-density11-sample-ordered-product · candidate

26. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(1)={0,…,0}, with recording=[0] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([0], [[0]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([0], [[0]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

27. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[2, 1, 2, 1] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([1, 2], [[1, 3], [0, 2]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([1, 2], [[1, 3], [0, 2]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

28. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-2, 0, -2, 2] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-2, 0, 2], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-2, 0, 2], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

29. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-3, 0, -3, 3] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-3, 0, 3], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-3, 0, 3], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

30. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-4, 0, -4, 4] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-4, 0, 4], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-4, 0, 4], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

31. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-5, 0, -5, 5] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-5, 0, 5], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-5, 0, 5], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

32. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-6, 0, -6, 6] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-6, 0, 6], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-6, 0, 6], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

33. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-7, 0, -7, 7] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-7, 0, 7], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-7, 0, 7], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

34. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-8, 0, -8, 8] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-8, 0, 8], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-8, 0, 8], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

35. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-9, 0, -9, 9] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-9, 0, 9], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-9, 0, 9], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

36. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-10, 0, -10, 10] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-10, 0, 10], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-10, 0, 10], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

37. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-11, 0, -11, 11] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-11, 0, 11], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-11, 0, 11], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

38. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-12, 0, -12, 12] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-12, 0, 12], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-12, 0, 12], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

39. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-13, 0, -13, 13] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-13, 0, 13], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-13, 0, 13], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

40. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-14, 0, -14, 14] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-14, 0, 14], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-14, 0, 14], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

41. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-15, 0, -15, 15] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-15, 0, 15], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-15, 0, 15], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

42. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-16, 0, -16, 16] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-16, 0, 16], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-16, 0, 16], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

43. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-17, 0, -17, 17] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-17, 0, 17], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-17, 0, 17], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

44. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-18, 0, -18, 18] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-18, 0, 18], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-18, 0, 18], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

45. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-19, 0, -19, 19] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-19, 0, 19], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-19, 0, 19], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

46. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-20, 0, -20, 20] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-20, 0, 20], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-20, 0, 20], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

47. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-21, 0, -21, 21] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-21, 0, 21], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-21, 0, 21], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

48. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-22, 0, -22, 22] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-22, 0, 22], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-22, 0, 22], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

49. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-23, 0, -23, 23] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-23, 0, 23], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-23, 0, 23], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

50. Recording Codes and Outcome Fibers

Elementary outcomes are Fin(4)={0,…,3}, with recording=[-24, 0, -24, 24] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.

View answer and explanation

([-24, 0, 24], [[0, 2], [1], [3]])

Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([-24, 0, 24], [[0, 2], [1], [3]]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-recording-image · candidate

51. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(1)={0,…,0}. Candidate raw list=[0]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([], [])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([], []).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

52. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(1)={0,…,0}. Candidate raw list=[]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([0], [])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([0], []).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

53. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(3)={0,…,2}. Candidate raw list=[0, 1, 2, 100]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([], [100])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([], [100]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

54. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(4)={0,…,3}. Candidate raw list=[0, 1, 2, -4]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([3], [-4])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([3], [-4]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

55. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(5)={0,…,4}. Candidate raw list=[0, 1, 2, 3, -5]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([4], [-5])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([4], [-5]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

56. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(6)={0,…,5}. Candidate raw list=[0, 1, 2, 3, 4, -6]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([5], [-6])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([5], [-6]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

57. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(7)={0,…,6}. Candidate raw list=[0, 1, 2, 3, 4, 5, -7]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([6], [-7])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([6], [-7]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

58. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(8)={0,…,7}. Candidate raw list=[0, 1, 2, 3, 4, 5, 6, -8]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([7], [-8])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([7], [-8]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

59. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(1)={0,…,0}. Candidate raw list=[-9]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([0], [-9])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([0], [-9]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

60. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(2)={0,…,1}. Candidate raw list=[0, -10]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([1], [-10])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([1], [-10]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

61. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(3)={0,…,2}. Candidate raw list=[0, 2, -11]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([1], [-11])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([1], [-11]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

62. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(4)={0,…,3}. Candidate raw list=[0, 1, 2, -12]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([3], [-12])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([3], [-12]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

63. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(5)={0,…,4}. Candidate raw list=[0, 1, 3, 4, -13]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([2], [-13])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([2], [-13]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

64. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(6)={0,…,5}. Candidate raw list=[0, 2, 3, 4, 5, -14]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([1], [-14])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([1], [-14]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

65. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(7)={0,…,6}. Candidate raw list=[1, 2, 3, 4, 5, 6, -15]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([0], [-15])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([0], [-15]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

66. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(8)={0,…,7}. Candidate raw list=[0, 1, 2, 3, 4, 5, 6, -16]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([7], [-16])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([7], [-16]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

67. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(1)={0,…,0}. Candidate raw list=[-17]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([0], [-17])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([0], [-17]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

68. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(2)={0,…,1}. Candidate raw list=[0, -18]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([1], [-18])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([1], [-18]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

69. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(3)={0,…,2}. Candidate raw list=[1, 2, -19]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([0], [-19])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([0], [-19]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

70. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(4)={0,…,3}. Candidate raw list=[0, 1, 2, -20]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([3], [-20])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([3], [-20]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

71. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(5)={0,…,4}. Candidate raw list=[1, 2, 3, 4, -21]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([0], [-21])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([0], [-21]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

72. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(6)={0,…,5}. Candidate raw list=[0, 1, 2, 4, 5, -22]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([3], [-22])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([3], [-22]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

73. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(7)={0,…,6}. Candidate raw list=[0, 2, 3, 4, 5, 6, -23]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([1], [-23])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([1], [-23]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

74. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(8)={0,…,7}. Candidate raw list=[0, 1, 2, 3, 4, 5, 6, -24]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([7], [-24])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([7], [-24]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

75. Missing and Outside Elementary Outcomes

Elementary outcomes are Fin(1)={0,…,0}. Candidate raw list=[-25]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

View answer and explanation

([0], [-25])

Compute the two directional differences; repetition cannot replace a missing outcome, and outside values are not elementary outcomes. No probabilities are specified. The exact result, retaining the requested order, is ([0], [-25]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-list-completeness-defects · candidate

76. Outcome and Event Membership Masks

Elementary outcomes are Fin(1)={0,…,0}, event E=[] is a subset of the space, and ordered candidates=[100, 101, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([No, No, No], [No, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([No, No, No], [No, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

77. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 101, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, No, No], [Yes, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, No, No], [Yes, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

78. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 4, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, No], [No, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, No], [No, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

79. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 4, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, No], [Yes, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, No], [Yes, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

80. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[100, 2, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([No, Yes, No], [No, Yes, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([No, Yes, No], [No, Yes, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

81. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 2, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, No], [No, Yes, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, No], [No, Yes, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

82. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 2, 102]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, No], [Yes, Yes, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, No], [Yes, Yes, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

83. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[100, 101, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([No, No, Yes], [No, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([No, No, Yes], [No, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

84. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 101, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, No, Yes], [No, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, No, Yes], [No, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

85. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 101, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, No, Yes], [Yes, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, No, Yes], [Yes, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

86. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[100, 4, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([No, Yes, Yes], [No, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([No, Yes, Yes], [No, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

87. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 4, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, Yes], [No, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [No, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

88. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 4, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, Yes], [Yes, No, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [Yes, No, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

89. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[100, 2, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([No, Yes, Yes], [No, Yes, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([No, Yes, Yes], [No, Yes, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

90. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 2, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, Yes], [No, Yes, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [No, Yes, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

91. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 2, 5]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, Yes], [Yes, Yes, No])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [Yes, Yes, No]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

92. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[100, 101, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([No, No, Yes], [No, No, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([No, No, Yes], [No, No, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

93. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 101, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, No, Yes], [No, No, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, No, Yes], [No, No, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

94. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 101, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, No, Yes], [Yes, No, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, No, Yes], [Yes, No, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

95. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[100, 4, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([No, Yes, Yes], [No, No, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([No, Yes, Yes], [No, No, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

96. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 4, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, Yes], [No, No, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [No, No, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

97. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[1, 4, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, Yes], [Yes, No, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [Yes, No, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

98. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[100, 2, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([No, Yes, Yes], [No, Yes, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([No, Yes, Yes], [No, Yes, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

99. Outcome and Event Membership Masks

Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 2, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, Yes], [No, Yes, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [No, Yes, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

100. Outcome and Event Membership Masks

Elementary outcomes are Fin(3)={0,…,2}, event E=[0, 1, 2] is a subset of the space, and ordered candidates=[0, 1, 2]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.

View answer and explanation

([Yes, Yes, Yes], [Yes, Yes, Yes])

Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [Yes, Yes, Yes]).

Reviewed step-by-step derivation

Sample space · qf-density11-sample-outcome-event-masks · candidate

Canonical question JSONL · English JSONL · Validation report